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Symmetry Group Analysis for Perfect Fluid Inhomogeneous Cosmological Models in General Relativity

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Abstract

In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between expansion scalar and shear scalar. For this, Lie group analysis is used to identify the generator (isovector fields) that leave the given system of PDEs (Einstein’s field equations) invariant for the models under consideration. A new class of exact solutions of Einstein’s field equation have been obtained for inhomogeneous space-time. The physical behaviors and geometric aspects of the derived models have been discussed in detail.

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Author notes

  1. Ahmad T. Ali

    Present address: Mathematics Department, Faculty Of Science, Al-Azhar University, Nasr City, 11884, Cairo, Egypt

Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, King Abdul Aziz University, PO Box 80203, Jeddah, 21589, Saudi Arabia

    Ahmad T. Ali

  2. Department of Physics, Anand Engineering College, Keetham, Agra - 282 007, India

    Anil Kumar Yadav

Authors
  1. Ahmad T. Ali
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  2. Anil Kumar Yadav
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Correspondence to Anil Kumar Yadav.

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Ali, A.T., Yadav, A.K. Symmetry Group Analysis for Perfect Fluid Inhomogeneous Cosmological Models in General Relativity. Int J Theor Phys 53, 2505–2519 (2014). https://doi.org/10.1007/s10773-014-2049-1

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  • DOI: https://doi.org/10.1007/s10773-014-2049-1

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